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Chapter 12: Q 14. (page 916)

In Exercise, provide a rough sketch of the graph of a function of two variables with the specified level “curve(s).”

One level curve consists of exactly two points.

Short Answer

Expert verified

One level curve consists of exactly two points.

Step by step solution

01

Step 1. Given information

One level curve consists of exactly two points.

02

Step 2. Explanation

The goal is to sketch a crude graph of a relationship of two variables with a "one level curve containing exactly two points."

The graph should have a single point at a value of z to have a single point as one of the level curves.

A spherical surface that finishes as a tip at the terminals of one of its diameters is one example.

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Most popular questions from this chapter

Prove that a square maximizes the area of all rectangles with perimeter P.

Consider the function f(x, y) = 2x + 3y.

(a) Why is the graph of f a plane?

(b) In what direction is f increasing most rapidly at the

point (−1, 4)?

(c) In what direction is f increasing most rapidly at the

point (x 0, y 0)?

(d) Why are your answers to parts (b) and (c) the same?

Find the gradient of the given function, and find the direction in which the function increases most rapidly at the specified point P.

f(x,y)=tan−1⁡yx,P=(−2,2)

In Exercises 21-28, find the directional derivative of the given function at the specified point Pand in the direction of the given unit vectoru .

f(x,y)=yxat P=(4,9),u=-1717,-41717

Use Theorem 12.32 to find the indicated derivatives in Exercises 21–26. Express your answers as functions of a single variable.

drdtwhenr=x2+y2,x=tandy=t2
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